Showing Hierarchy / Project view during UV editing
Blender's UI allows us to split the window into multiple sections, each using a different editor. These window layouts are saved as a list of Screens which we can switch between and add to. The default UV editing screen does not provide an outliner, or a graph editor or a properties editor or dopesheet...

There are three places that screens can be defined, the default screens programmed into blender, the startup blend that has your settings or each blend file that you use. When you open a blend file there is a Load UI option which decides if you want to use the screens in the file you are opening or keep the screens you are currently using. You can set the default for this option in the preferences.

Every time you adjust the window layout you are altering the current screen and that adjustment is kept in the current screen and saved with the blend file. If you don't like the default screens that blender provides you can define your own screen layouts.

You define custom layouts by starting blender, create and adjust as many screens as you want and then save your startup blend. This makes them available every time you start blender, if you also disable the Load UI option in preferences and save that you will use your layouts unless you choose to use the layouts in the file as you open it.